Ab initio phase stabilities of Ce-based hard magnetic materials and comparison with experimental phase diagrams

Abstract

Recent developments in electrical transportation and renewable energies have significantly increased the demand of hard magnetic materials with a reduced critical rare-earth content, but with properties comparable to (Nd,Dy)-Fe-B permanent magnets. Though promising alternative compositions have been identified in high-throughput screenings, the thermodynamic stability of these phases against decomposition into structures with much less favorable magnetic properties is often unclear. In the case of Ce-Fe-Ti alloys, we have used finite temperature ab initio methods to provide this missing information. Employing state-of-the-art approaches for vibrational, electronic, and magnetic entropy contributions, the Helmholtz free energy, $F(T,V)$, is calculated for the desired hard magnetic ${\mathrm{CeFe}}_{11}\mathrm{Ti}$ phase and all relevant competing phases. The latter have been confirmed experimentally by employing reactive crucible melting (RCM) and energy-dispersive x-ray spectroscopy (EDS). Our ab initio based free energy calculations reveal that the presence of the ${\mathrm{CeFe}}_{2}$ Laves phase suppresses the formation of ${\mathrm{CeFe}}_{11}\mathrm{Ti}$ up to 700 K. The result is in agreement with RCM, in which ${\mathrm{CeFe}}_{11}\mathrm{Ti}$ is only observed above 1000 K, while the ${\mathrm{CeFe}}_{2}$ and ${\mathrm{Ce}}_{2}{\mathrm{Fe}}_{17}$ phases are stable at lower temperatures.